AP Physics 2: Ideal Gas Law & PV Diagrams

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Conceptual illustration of Thermodynamics: A microscopic view of gas molecules colliding in a container alongside a macroscopic view of a piston and a PV diagram.

In AP Physics 2, we shift our focus from individual moving objects to macroscopic systems. Understanding how billions of gas molecules create pressure and temperature is the foundation of Unit 9: Thermodynamics. This unit accounts for 12–15% of your total exam score.

1. Kinetic Molecular Theory (KMT)

To predict gas behavior, we use the Ideal Gas Model. We assume gas particles are in constant, random motion and undergo perfectly elastic collisions. The most critical link you must remember for the AP exam is that Absolute Temperature is proportional to the average kinetic energy of the particles.

$K_{avg} = \frac{3}{2} k_B T = \frac{1}{2} m v_{rms}^2$

Higher temperature means faster-moving molecules.

Maxwell-Boltzmann distribution graph showing the probability of molecular speeds at two different temperatures. The curve for the higher temperature is flatter and shifted to the right.

Speed Distribution: Not all molecules move at the same speed. As temperature increases, the distribution flattens and shifts toward higher velocities.

2. The Ideal Gas Law

The state of a gas is determined by its Pressure ( $P$ ), Volume ( $V$ ), and Temperature ( $T$ ). While chemistry students use $PV=nRT$ , physics students often use the version with the total number of molecules ( $N$ ).

$PV = nRT \quad \text{or} \quad PV = N k_B T$

Remember: $T$ must always be in Kelvin ( $K = ^\circ C + 273$ ).

Key Relationships:

Boyle’s Law: If $T$ is constant, $P$ is inversely proportional to $V$ (squeeze a gas, pressure goes up).
Charles’s Law: If $P$ is constant, $V$ is directly proportional to $T$ (heat a gas, it expands).
Gay-Lussac’s Law: If $V$ is constant, $P$ is directly proportional to $T$ (heat a gas in a rigid box, pressure goes up).

3. Mastering PV Diagrams

A PV Diagram is a map of a gas system’s journey. By looking at a graph of Pressure vs. Volume, you can determine if the system is gaining energy or doing work.

A Pressure vs. Volume graph showing four processes: Isobaric (horizontal), Isochoric (vertical), Isothermal (curved), and Adiabatic (steeper curve).

The Four Fundamental Processes: Tracking how a gas changes state. The area under any process curve equals the Work ( $W$ ) done by the system.

Common Thermodynamic Processes:

Isobaric: Constant Pressure. A horizontal line. Work is easily calculated as $P\Delta V$ .
Isochoric: Constant Volume. A vertical line. Since there is no displacement, Work is zero.
Isothermal: Constant Temperature. A curved path where $PV$ remains constant. Here, $\Delta U = 0$ .
Adiabatic: A steeper curve. No heat is exchanged ( $Q = 0$ ).

⚠️ The “Area” Trick: On the AP Physics 2 exam, if you are asked to find the work done during a cycle, simply calculate the area enclosed by the path on the PV diagram.

4. Quick AP Practice

📚 AP Practice Problems

1. If the absolute temperature of an ideal gas is tripled, what happens to the average kinetic energy of the molecules?

Answer

Since $K_{avg} \propto T$ , tripling the temperature results in tripling the average kinetic energy.

2. Look at the PV diagram above. In an Isochoric process, how much work is done by the gas?